Mads methods

# **MADS** Methods * [Model analyses](#model-analyses) * [Decision support](#decision-support) * [Contaminant transport simulators](#contaminant-transport-simulators) * [Test functions](#test-functions) ### Model analyses **MADS** includes a wide range of techniques for model-based analyses that can perform local and global exploration of model parameter space: * Optimization techniques for Parameter Estimation (**PE**), Model Inversion, Model Calibration, and Decision Support (**DS**) * Several different implementations of the local Levenberg-Marquardt (**LM**) optimization technique: [GSL](http://www.gnu.org/s/gsl/), [IMSL](http://www.roguewave.com/products/imsl-numerical-libraries.aspx), [LevMar](http://www.ics.forth.gr/~lourakis/levmar/). The Levenberg-Marquardt (**LM**) optimization technique can be performed using [acceleration and delayed gratification approaches](http://link.aps.org/doi/10.1103/PhysRevE.83.036701). In **LM**, the inversion of Jacobian (sensitivity) matrix can be performed using a wide range of techniques: BK (Bunch and Kaufman), LU, QR, QRLS, Cholesky, and SVD (singular value) decompositions using LAPACK and SVDPACK libraries. **SVD decomposition** allows for highly-parameterized inversion where the number of model parameters is substantially greater than the number of model constraints (calibration targets or model observations); a similar approach is called [SVD-assist](http://www.pesthomepage.org/Highly-parameterized_inversion.php) in [PEST](http://www.pesthomepage.org). * Multi-Start Levenberg-Marquardt (**MSLM**) optimization technique * Global Particle Swarm Optimization ([PSO](http://clerc.maurice.free.fr/pso/)) * Global Adaptive Particle Swarm Optimization [TRIBES](http://www.particleswarm.info/Tribes_2006_Cooren.pdf) * Global Optimization technique coupling Particle Swarm and Levenberg-Marquardt optimization technique [SQUADS](papers/squads_v04.pdf) * Sensitivity Analysis (**SA**) techniques * Global Monte-Carlo based analysis * Local eigen analysis of Jacobian matrix of model parameters * [Sobol's global sensitivity indices](http://www.mlmatrix.com/uploadfile/200712418203522.pdf) * Agent-based Global Uncertainty and Sensitivity [ABAGUS](papers/Harp & Vesselinov ABAGUS 2011.pdf) analysis * Sampling (design of experiment) techniques (based on random or user provided seed): * Pseudo random sampling * Latin-Hypercube sampling techniques: random, center, edge * [Improved Distributed Hypercube Sampling](http://people.sc.fsu.edu/~jburkardt/datasets/ihs/ihs.html) (**IDLHS**; aka **IHS**) * Uncertainty Quantification (**UQ**) techniques * Global Monte-Carlo based analysis * Local analysis based on Jacobian matrix of model parameters * Agent-based Global Uncertainty and Sensitivity [ABAGUS](papers/Harp & Vesselinov ABAGUS 2011.pdf) analysis ### Decision support **MADS** includes methods for Model-based Decision Support (**DS**) * Bayesian analysis utilizing [DREAM](http://www.biometris.wur.nl/UK/Staff/Cajo+ter+Braak/Software+and+Data/DE-MC+and+DREAM+software+page/) * non-Bayesian analysis utilizing [minimax](http://www.sciencedirect.com/science/article/pii/S0004370206000245), [info-gap](papers/Harp & Vesselinov infogap source 2011.pdf) and [GLUE](http://www.sciencedirect.com/science/article/pii/S0022169401004218) * Global Optimization technique coupling Particle Swarm and Levenberg-Marquardt optimization techniques [SQUADS](papers/squads_v04.pdf) * Agent-based Global Uncertainty and Sensitivity [ABAGUS](papers/Harp & Vesselinov ABAGUS 2011.pdf) analysis ### Contaminant transport simulators **MADS** includes several analytical simulators for representation of 3D contaminant transport in aquifers. The analytical simulation is based on the solutions developed by [Wexler (1992)](http://pubs.usgs.gov/twri/twri3-b7/) and [Park & Zhan (2001)](http://www.sciencedirect.com/science/article/pii/S016977220100136X). The solutions are solved using [GSL](http://www.gnu.org/s/gsl/) subroutines. Alternative solutions are available for contaminant sources with different geometry: * point source * plane source (along the top of the aquifer) * 3D box (straight parallelepiped) source ### Test functions **MADS** includes a series of test functions that can be applied for efficient testing of model-analysis and decision support techniques. These test functions are commonly used in the practice. The list of all the test functions built-in in **MADS** are listed in the [manual](mads-manual.md)